How to deal with infinite integrals in quantum field theory

Infinite integrals arising in perturbative expansions to quantum field theory have to be defined by means of a regularization procedure before they can be cancelled by a renormalization of the physical parameters in the theory. After a rapid survey of traditional regularization schemes fairly recent developments relying on point-splitting, non-polynomial interactions, analytic regularization and dimensional continuation are described. Among various critical tests of the schemes vacuum polarization, scattering in an external field and the axial anomaly are considered. (author)